IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry

gegsps

what r the coordinates of centroid of the triangle formed by the LINES X2+4XY+Y2=0 AND X+Y=1?

gunshot

what st lines

gegsps

anyone please reply plz plz

Aatish

See buddy.......

${x}^{2}+4xy+{y}^{2} = 0$

represents a pair of straight lines.....

factorizing it and getting the two lines.......as,...........

$(x + y(2 + \sqrt{3}))(x + y(2 - \sqrt{3})) = 0$

so the two lines are.........

$x+y(2+\sqrt{3}) = 0\\x+y(2-\sqrt{3}) = 0$

and the third one is given........

x + y =1..........

solve these three equations.....get the three vertices of the triangle formed by them.......

and then use this formula for getting the coordinates of the centroid,,,,,,,,,

$(x,y) = (\frac{{x}_{1}+{x}_{2}+{x}_{3}}{3},\frac{{y}_{1}+{y}_{2}+{y}_{3}}{3})$

hope u can do the calcs........

cheers........